"drink it up" is correct and usable in written English.
You can use it when you want to encourage someone to drink something up quickly, or when you want to share something that is enjoyable and should be savored. For example: "This hot cocoa is so delicious, so drink it up while it's still warm!".
So right about now, Microsoft is wielding an old wooden bowling pin, wiping its chin, and ranting, "I drink it up!" (Milkshake photo by Dion Gillard).
"We'll turn around and either drug it up or drink it up".
"Teen-agers drink it up so fast, we've gotta pour refills every five minutes," she said.
You drink it up, take it away, and write about it at a later day.
At a talk given recently at the Kitchen in Chelsea, she advised listeners how to approach her work: "I want you to drink it up with your eyes and your mind".
A genuine note of excitement seeps into Omar's guarded badinage when he describes giving oral sex as "feeling the power of all creation fill you up until you are all creation" and "just losing yourself in the fact that you are right up there in the gate of fucking life, and you get to drink it up all you want".
The table, still so natural looking, still so much a tree, drank it up like a living thing.
He drinks your milkshake – he drinks it up – and then goes onto win Oscars for his performances in films like "There Will Be Blood" and "My Left Foot".
"My mother gave my father $25 to buy cigarettes, but he drank it up," Chris explains, affronted, but evidently sensitive to the irony.
To her surprise, her son drank it up quickly and satisfyingly.
"All my friends drank it up, and it starting to feel odd being the only person in line (besides my friend Tom) who was buying MyDrink anymore…Over time, I think I got too comfortable with it.
